A novel similitude method for predicting natural frequency of FG porous plates under thermal environment

Abstract

For FG porous plates under thermal environment, the complexity of porosity leads to the inaccuracy of theoretical analysis, so it is important to establish dynamic similitude to guide the scaled model test to reduce the difficulty and cost of thermal vibration test. For the first time, the dynamic similitude of FG porous plates under thermal environment is studied in this paper. To solve the similitude distortion caused by non-scalability of FGM and the porosity, a novel similitude method is proposed and the predictive formula of natural frequency is derived. The highlight is that the consideration of porosity distribution in this paper does not depend on any artificial simplified assumption, and is suitable for the actual and unknown porosity distribution; meanwhile, the influences of heat conduction, thermal expansion and material properties varying with temperature are comprehensively considered without any simplified assumption. Through various numerical cases with different temperature conditions and porosity distributions, the compared results with good agreement verify the correctness and wide applicability of the proposed method and derived formula. The derived predictive formula clearly reveals the inherent law of natural frequency varying with length/width of plates. Relying on the proposed method and derived formula can reduce tests of models with different sizes, which greatly facilitates the accumulation of database.

Highlights

• For the first time, the dynamic similitude of FG porous plates under thermal environment is studied.

• To solve the similitude distortion caused by non-scalability of FGM and the porosity, a novel similitude method is proposed.

• The derived predictive formula of natural frequency clearly reveals the inherent law of natural frequency varying with length/width of plates.

• The consideration of porosity distribution in this paper does not depend on any artificial simplified assumption, and is suitable for the actual and unknown porosity distribution.

• The influences of heat conduction, thermal expansion and material properties varying with temperature are comprehensively considered without any simplified assumption.

Keywords:

• FG plates
• porous
• thermal environment
• dynamic similitude
• scaled model
• similitude distortion
• energy similitude correction method

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.